Graphs of Equations Objectives: Find intercepts from a Graph Find intercepts from an Equation Test an Equation for Symmetry with Respect to the x-axis, y-axis and origin

Intercepts The points, if any, at which a graph crosses or touches the coordinate axes. (x-intercept and y-intercept) To find the x-intercept(s), if any, of the graph of an equation, let y = 0 in the equation and solve for x. To find the y-intercept(s), if any, of the graph of an equation, let x = 0 in the equation and solve for y. X-intercepts are also called the Zeros or Roots of the equation

EX: Find the intercepts of the graph or equation 1. 2. 3.

Symmetry Symmetric with respect to the x-axis: if for every point (x,y) on the graph there is a point (x,-y) also on the graph TEST an Equation: Replace y by –y in the equation. If an equivalent equation results, the graph of the equation is symmetric to the x-axis. Symmetric with respect to the y-axis: if for every point (x,y) on the graph there is a point (-x,y) also on the graph TEST an Equation: Replace x by –x in the equation. If an equivalent equation results, the graph of the equation is symmetric to the y-axis. Symmetric with respect to the origin: if for every point (x,y) on the graph there is a point (-x,-y) also on the graph TEST an Equation: Replace x by –x and y by –y in the equation. If an equivalent equation results, the graph of the equation is symmetric with the origin.

EX: Tell whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin 4. 5. 6.

EX: Determine whether the given points are on the graph of the equation